Problem: Simplify; express your answer in exponential form. Assume $r\neq 0, z\neq 0$. $\dfrac{{(r^{4})^{4}}}{{(rz)^{-5}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${r^{4}}$ to the exponent ${4}$ . Now ${4 \times 4 = 16}$ , so ${(r^{4})^{4} = r^{16}}$ In the denominator, we can use the distributive property of exponents. ${(rz)^{-5} = (r)^{-5}(z)^{-5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(r^{4})^{4}}}{{(rz)^{-5}}} = \dfrac{{r^{16}}}{{r^{-5}z^{-5}}}$ Break up the equation by variable and simplify. $\dfrac{{r^{16}}}{{r^{-5}z^{-5}}} = \dfrac{{r^{16}}}{{r^{-5}}} \cdot \dfrac{{1}}{{z^{-5}}} = r^{{16} - {(-5)}} \cdot z^{- {(-5)}} = r^{21}z^{5}$.